In k-means clustering, the following expression is evaluated
$$ \arg \min \sum_{i=1}^k \sum_{x \in \bf{S}_i} \left|\left| \bf{x}-\bf{\mu}_ i \right|\right|^2$$
Why is the taking the norm required when $\bf{x}-\bf{\mu}$ is squared anyway? Is the norm required, because without it would not be explicit, that it's a distance between two vectors which is squared?
A vector cannot be squared. Real numbers can.
That being said, life would of course be miserable without canonical (!) implicit notation. Squaring a vector, however, is not canonical at all. Indeed, I would bet that no one has ever used that notation in an article. For a good reason: the norm to be squared might not be obvious, and some might also think squaring a vector means taking the square of each component.